Question

A 17-year annuity pays $1,600 per month, and payments are made at the end of each month. The interest rate is 11 percent compounded monthly for the first six years and 9 percent compounded monthly thereafter.

  

What is the present value of the annuity?

• $153,407.29

• $150,339.14

• $156,475.43

• $217,830.03

• $1,840,887.45

Answer 1

Answer : Correct Option is 153,407.29

Reason :

Calculation of present value of Annuity :

For the prupose of calculating Present value of Annuity we first need to calculate present value for the years after 6 years i.e 11 years (17 - 6 ) with  9 percent compounded monthly using PV function of Excel :

=PV(rate,nper,pmt,fv)

here,

rate is the rate of interest per period i.e 9% / 12 = 0.75% (As there monthly compounding and there are 12 months in a year therefore divided by 12)

nper is the number of Payments i.e 11 (17 - 6 ) * 12 = 132 (As there monthly compounding and there are 12 months in a year therefore multiplied by 12)

pmt is the periodic payment i.e 1600

fv is the future value which will be 0

=PV(0.75%,132,-1600,0)

Therefore present value of payment from 6th to 17th year is 133,770.27

Now we will calculate present value as a whole taking the present value of the above amount calculated above, for remaining payment (i.e for starting 6 years)

=PV(rate,nper,pmt,fv)

here,

rate is the rate of interest per period i.e 11% / 12 = 0.9166667% (As there monthly compounding and there are 12 months in a year therefore divided by 12)

nper is the number of Payments i.e 6 * 12 = 72 (As there monthly compounding and there are 12 months in a year therefore multiplied by 12)

pmt is the periodic payment i.e 1600

fv is the future value which will be the amount calculated i.e 133770.27

=PV(0.916666667%,72,-1600,-133770.27)

Therefore present value of payment of Annuity is $153,407.29